[Grammar] Either/each hand

[RIKZ]

Hello!
A few days ago I've passed my A-level exam of English. There was one sentence, that I want to ask about.
"He entered a room holding a briefcase in ... hand." Instead of ellipsis there was a word that literually translates (from Russian) as "both". I understood, that "both" not correct here (because "in both handS") and I wrote down "each" (remembering phrase "in each hand"). I still don't know if it's correct or not, but in other variants the correct answer in this task was "either" and the answer is always the same for all variants. So, I've googled and founded nothing about phrase in either hand, is it even possible to say so? And in this sentence especially?
Thanks for answer in advance.

 

[Rover_KE]

Welcome to the forum, RIKZ.

Congratulations on your exam success and on your nearly perfect post.

In this context, you can use either 'either' or 'each' with no difference in meaning.

 

[jutfrank]

I don't understand. You're saying that in your English exam (not actually an A-level but I presume the Belarus equivalent) they gave you a sentence in English which contained a Russian word? Is that right?

 

[RIKZ]

I don't understand. You're saying that in your English exam (not actually an A-level but I presume the Belarus equivalent) they gave you sentence in English which contained a Russian word? Is that right?

That's right. The task was to translate that word from Russian into English.
Actually, A-level exam called Central Testing here.

 

[jutfrank]

In this context, you can use either 'either' or 'each' with no difference in meaning.

Really?

It really doesn't sound right to me with either, and neither does it make sense. Possibly because I would never say that. Do you think this is possibly an old-fashioned use of either?

He's carrying two briefcases, right? One in each hand. The better answer by far is each, in my opinion.